Senate Majority Leader Harry Reid of Nevada, left, comments to journalists as he takes the elevator after a rare Senate session on Capitol Hill in Washington on Sunday. Senate Republicans and Democrats hit an impasse Sunday over spending in their last-ditch struggle to avoid an economy-jarring default in just four days and end a partial government shutdown that’s entering its third week.

WASHINGTON — Senate Republicans and Democrats hit an impasse Sunday over spending in their last-ditch struggle to avoid an economy-jarring default in just four days and end a partial government shutdown that’s entering its third week.

After inconclusive talks between President Barack Obama and House Republicans, Senate Majority Leader Harry Reid, D-Nev., and Minority Leader Mitch McConnell, R-Ky., took charge in trying to end the crises, although a conversation Sunday afternoon failed to break the stalemate.

“I’m optimistic about the prospects for a positive conclusion to the issues before this country today,” Reid said as the Senate wrapped up a rare Sunday session.

The two cagy negotiators are at loggerheads over Democratic demands to undo or change the automatic, across-the-board spending cuts to domestic and defense programs that the GOP see as crucial to reducing the nation’s deficit.

McConnell insisted a solution was readily available in the proposal from a bipartisan group of 12 senators, led by Sens. Susan Collins, R-Maine, and Joe Manchin, D-W.Va., that would re-open the government and fund it at current levels for six months while raising the debt limit through Jan. 31.

“It’s time for Democrat leaders to take ‘yes’ for an answer,” McConnell said in a statement.

But six Democrats in the group and a spokesman for Collins said that while negotiations continued this weekend, there was no agreement.

The latest snag comes as 350,000 federal workers remain idle, hundreds of thousands more work without pay and an array of government services, from home loan applications to environmental inspections, were on hold on the 13th day of the shutdown.

Many parks and monuments remain closed, drawing a protest at the National World War II Memorial on Sunday that included tea party-backed lawmakers who had unsuccessfully demanded defunding of President Barack Obama’s 3-year-old health care law in exchange for keeping the government open.

Unnerving to world economies is the prospect of the United States defaulting on its financial obligations on Thursday if Congress fails to raise the borrowing authority above the $16.7 trillion debt limit.

Christine Lagarde, the International Monetary Fund’s managing director, spoke fearfully about the disruption and uncertainty, warning of a “risk of tipping, yet again, into recession” after the fitful recovery from 2008. The reaction of world financial markets and the Dow Jones today will influence any congressional talks.

Congress is racing the clock to get a deal done, faced with time-consuming Senate procedures that could slow legislation, likely opposition from tea partyers and certain resistance in the Republican-led House before a bill gets to Obama.

Politically, Republicans are reeling, bearing a substantial amount of the blame for the government shutdown and stalemate.

“We’re in a free-fall as Republicans, but Democrats are not far behind,” said Sen. Lindsey Graham, R-S.C., in warning Democrats about seizing on the GOP’s bruised brand as leverage to extract more concessions.

McConnell and Republicans want to continue current spending at $986.7 billion and leave untouched the new round of cuts in January, commonly known as sequester, that would reduce the amount to $967 billion. Democrats want to figure out a way to undo the reductions, plus a long-term extension of the debt limit increase and a short-term spending bill to reopen the government.

“Republicans want to do it with entitlement cuts,” said Sen. Chuck Schumer, D-N.Y. “Democrats want to do it with a mix of mandatory cuts, some entitlements and revenues. And so how do you overcome that dilemma? We’re not going to overcome it in the next day or two.”

He suggested keeping the government running through mid-January.

Sen. Dick Durbin of Illinois, the No. 2 Democrat in the Senate, told reporters the two sides are roughly $70 billion apart, the difference between the $1.058 trillion Senate budget amount and the $988 billion envisioned by House Budget Committee Chairman Paul Ryan, R-Wis.

“We haven’t picked a number, but clearly we need to negotiate between those two,” Durbin said.

Republicans dismiss the latest request as Reid moving the goalposts in negotiations as they were getting closer to resolving the stalemate that has paralyzed Washington. They also argue that it is disingenuous for Democrats to resist any changes in the 3-year-old health care law while trying to undo the 2011 budget law that put the cuts on track.

“I think the Democrats are on the verge of being one tick too cute as they see the House possibly in disarray — they now are overreaching, and I think that what we’ve got to do is get this back in the middle of the road, act like adults,” said Sen. Bob Corker, R-Tenn.

Graham and Sen. Rand Paul, R-Ky., said they would not support any deal that upends the spending limits imposed by the 2011 law, and predicted that their Senate GOP colleagues would oppose it as well.

Out of play, for now, was the Republican-led House, where Speaker John Boehner, R-Ohio, told GOP lawmakers early Saturday that his talks with the president had ground to a halt. Obama telephoned House Democratic leader Nancy Pelosi on Sunday, focusing on the need for any increase in the debt limit without concessions.

Also sidelined, at least for now, was the plan forged by Collins and a bipartisan coalition to briefly fund the government and extend the $16.7 trillion debt limit, in exchange for steps like temporarily delaying the medical device tax that helps fund the health care law.

Democrats said Collins’ plan curbed spending too tightly, and Reid announced Saturday it was going nowhere.

Collins said Sunday that both Democrats and Republicans continue to offer ideas and say they want to be part of the group working to reopen the government and address the debt ceiling before Thursday’s deadline.

“We’re going to keep working, offering our suggestions to the leadership on both sides of the aisle in an attempt to be constructive and bring this impasse to an end. Surely we owe that to the American people,” Collins said.

Sen. Amy Klobuchar, D-Minn., a participant in Collins’ talks, said Reid wouldn’t accept everything in the Collins proposal, but he “knows there are some positive things in that plan,” such as opening the government in a “smart timeframe,” not defaulting on debt and doing something in the long term on the budget.

Klobuchar and Collins were on CNN’s “State of the Union.” Graham appeared on ABC’s “This Week,” Corker was interviewed on “Fox News Sunday,” Schumer spoke on CBS’ “Face the Nation” and Lagarde was on NBC’s “Meet the Press.”